看昌海兄新作《Lee Smolin 和他的“The Trouble with Physics”》看得惊涛骇浪，十分过瘾~这篇文章实在气势磅礴，对于该文章有一下几点不同意见和补充意见。其他评论以后继续写。

“那么 Smolin 会因为在弦论如日中天时写下过的这部著作， 而被物理学史所纪录”
我无法同意这个观点，事实上，超弦现在似乎不是如日中天，一次革命和二次革命才是如日中天的时候，但是离现在已经很远。现在的弦论在物理上进展不快，或许数学上总有突破。从这一点来看，Smolin其实是想占“痛打落水狗”的便宜。真正如日中天的时候，估计这厮正在公开或者偷偷研究弦论，不然他怎么可能写出一些技术性评论呢，呵呵。

Smolin或许会因为写出这部著作而被“物理学评论史”纪录，但是不会因为这样一部本质上推销自己的圈量子引力的书而被物理学史纪录。因为这种攻讦本身不是物理。

Smolin说很多人太顺从Witten，正如昌海兄所反驳的那样，很多重要思想是其他人提出的。例如D-Brane，AdS-CFT对应，分别是Polchinski和Maldacena的杰作，而Witten只是在这些理论提出后迅速推广加深。不知道Smolin怎么这么喜欢拿着一些跟风者说事。何况，现在搞GR-QC的人不是很多人都喜欢跟随Einstein的几何精神和Hawking的几何技巧吗？难不成也要说这些人都是白痴。而且Hawking不也对AdS-CFT对应研究得津津有味吗？Smolin的极端现实出他的短浅和狭隘。

或许Smolin一直因为圈量子引力不如超弦受欢迎而愤恨，所以主张非主流。那么当超弦被打倒，圈量子引力上台成为主流后，我们也是否要重新高举非主流的旗帜打倒圈量子引力？看超弦不爽就直接攻击其弱点，何必拿着主流非主流做文章？垃圾理论，就算是非主流，也别指望咸鱼翻身，一些非主流理论后来成为主流不等于所以非主流理论都将成为主流，一个人摸中六合彩不等于所有人都有这运气。Smolin逻辑如此混乱却硬要当物理学法官，这个嘴脸够可笑。其实他和Woit也差不多了，人家Woit还不像他那样借着骂超弦之机以“王婆卖瓜，自卖自夸”的方式来推销圈量子引力呢。

谢谢萍踪兄的评论，先赠一张美女相片表示感谢。

我最后那段话是从一个假想的未来角度来评论的。弦论自二次革命之后虽未出现可与两次革命相比的重大进展，但从其在基础研究中占据的地位来看，始终还在高位上。如果弦论最终衰落了，那么用将来的眼光看，从二次革命到现在应该都可以算如日中天的时期，衰落应该是后来发生的事－比如超对称被实验排挤到越来越高的能区（我始终觉得如果超弦最终衰落，这是最可能的原因，因此在最后一段特意点了一下）。Smolin同志的书在那种情况下估计会被记录（不过萍踪兄说得也不错，他这部书从物理本身来讲是够不上被记录的标准的，能赌的只是时机），我本来想说这本书可以算是Smolin同志的一场小赌，而且赌赢的可能性比他的物理大，后来还是决定写得客气点。回家后我打算将那段话的语气改得更模糊一点（因为那毕竟只是对未来的臆测）。

衰落应该是后来发生的事－比如超对称被实验排挤到越来越高的能区

I don't think this is and will be the real reason. It is the fact that there is no real breakthrough, one similar to AdS-CFT, in string theory for a number of years now. Although it is well defined in perturbative vacua, we do not know the real relevant degrees of freedom.

Anyway, relevant or not, string theory is a beautiful and consistent construction . Studying of it, even as toy models, has brought very useful insights into quantum theories.

In comparison, loop quantum gravity is not even qualified to be called a theory since there is even no consistent framework yet.

:: It is the fact that there is no real breakthrough

This is certainly a major possibility as well. The reason I didn't make this my top bet is because this kind of death will be a slow one. Any particular direction inside string theory might die this way within a few years, but it's going to take a long time for the whole theory to die. In the mean while, experimentalists might be able to raise the lower bound of susy breaking scale enough to dramatically reduce the attractiveness of susy in physics, which in turn may affect string theory, and dramatically accelerates its death.

Of course, guess is only guess, susy might turn out to be a correct idea. In that case, if string theory still dies, I will also bet on no real breakthrough as the most probable reason.

呵呵，谢谢昌海兄赠送的《黄真伊》剧照，非常漂亮：）

我个人觉得，SUSY breaking的能标如果被越推越远，还不至于直接宣示弦论的失败，因为可以修正一些参数来对付高能实验对能区的排除，因为SUSY的各个模型中，参数还是很自由的，人们对于参数的选择很大程度上也因为TeV能标的破缺比较符合级列问题的解决，可以避免fine-tuning问题的卷土重来，而不见得非得在什么样的能标上破却。

比较离奇的是，有弦论学者甚至认为弦论即使是在SUSY被排除时仍然不落败。如果这样的话，SUSY的作用何在？仅仅为了消除一些发散和反常吗？

的确如sage兄所说，弦论即使作为玩具模型也是具有巨大价值的，对于QFT理论的深刻认识和对数学方法的促进作用是极其巨大的。而圈量子引力让我看见的只有丑陋。

文章看了，弦论的确过于popular了，连一个seminar都可以吸引一些非专业人士来看看（多半是第一次seminar)。不少读研究生的学生一进来选导师也很希望做弦论，然后就发现弦论远不是想的那么回事，然后就跑去做宇宙学了。
相对弦论获得的关注而言，它产出的结果不成正比。
我不相信弦论是个最终的理论，因为对我来说，它还不够racial,对基础修改的太少了，把点换成弦并不能提供观念上颠覆性的突破。它是一个很好的数学玩具，但是我不相信它的物理解释。它的结果在我的价值判断里也还不够crazy，与QM和GR不同，daily life和我们对世界最根本的认识也没有因为string而改变。string正在使越来越多的人丧失信心。

:: SUSY breaking的能标如果被越推越远，还不至于直接宣示弦论的失败

是的，要从实验上彻底否证弦论，在可预见得到的将来都是几乎不可能的。因此我在回帖中只是说 susy breaking 能标的提高可能会 “dramatically reduce the attractiveness of susy in physics, which in turn may affect string theory”。 超对称破缺的能标被推得越高，原先人们希望它干的好事，它就会干得越来越少，而且会干得越来越不漂亮。这将影响物理学家们对它的兴趣和信心，而这极有可能会波及弦论。

TeV 是一个不太遥远的能标，现在从事物理的学生应该会有这个幸运看到这个能标上的事情，无论susy在这个能标上被证实与否，都会有事情可做。

:: 比较离奇的是，有弦论学者甚至认为弦论即使是在SUSY被排除时仍然不落败。
:: 如果这样的话，SUSY的作用何在？仅仅为了消除一些发散和反常吗？

susy 在弦论中的主要作用有两大类： 一是消除tachyon（以及由此导致的发散等）， 二是帮助研究非微扰性质等。 其中第一类是必须解决的， 第二类则是技术上的便利。

弦论学家有一种设想，那就是通过 tachyon condensation 化解 tachyon 造成的问题，并给出一种类似 Higgs 机制那样的好东西，不过目前似乎尚未有具体的实现手段。 假如这有可能实现， 那么弦论在没有 susy 时所面临的最大障碍就有可能被消除。 从这个意义上讲， 没有 susy 的确不等同于弦论的失败。

但如果真的没有 susy (而不仅仅是破缺能量很高)， 那么今天炙手可热的那些非微扰结果， 包括许多对偶性， 大都得完蛋。 这虽只是技术困难， 但今天的超弦尚且如此困难， 没有 susy 的弦论将比今天的超弦还要困难得多， 而且其数学魅力也要减弱很多， 这同样可能造成弦论的衰落。

BTW, as we are talking more about technical issues, I moved it to academic forum.

：：但如果真的没有 susy (而不仅仅是破缺能量很高)， 那么今天炙手可热的那些非微扰结果， 包括许多对偶性， 大都得完蛋。 这虽只是技术困难， 但今天的超弦尚且如此困难， 没有 susy 的弦论将比今天的超弦还要困难得多， 而且其数学魅力也要减弱很多， 这同样可能造成弦论的衰落。
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的确，如果没有SUSY，那么超弦就名不副实，因为那是建立在超对称之上的。对偶性质也几乎都要完蛋，这样的弦论即使活着，也算是高位截瘫了。何况新的tachyon消除机制既无试验依据，更无SUSY那样的理论优雅，如果SUSY如同刘备那样挂掉，那么后备的tachyon消除机制可能就是阿斗那样更是糟糕。
从这一点看，超弦的很多人对于这个理论强烈以来SUSY表现得非常焦虑，因为一旦SUSY完蛋，那几乎就是把超弦连根摧毁。至少SUSY的最早起源恰恰是源自弦论。

另外一点，超弦现在虽然还在撑着，但是已经在物理上处于停滞，过去人们对它的热望现在几乎已经变成观望，因此，若把现在这样的状态也归为鼎盛，那么超弦要么一直这样鼎盛下去，要么就直接完蛋，而不会有所谓的平凡时期了。当然，或许伴随着SUSY的被证实，超弦也会跟着走向更加鼎盛的状态（毕竟SUSY是它的直接产物）。

:: 超弦现在虽然还在撑着，但是已经在物理上处于停滞，过去人们对它的热望
:: 现在几乎已经变成观望，因此，若把现在这样的状态也归为鼎盛，那么超弦
:: 要么一直这样鼎盛下去，要么就直接完蛋，而不会有所谓的平凡时期了

我对弦论在最终衰落的情况下的衰落方式的猜测大致如上图所示（不要注意微小的起伏，那是我的手在颤抖，并无深意-用鼠标画曲线真难:-）。绿色表示不考虑susy实验因素（即一直象现在这样纯理论地走下去又无法与实验实质接触），蓝色表示如果某个时刻susy能标被抬高到令人失去兴趣的程度，黄色表示某个时刻susy被发现。二次革命之前，弦论有一段所谓的黑暗期，据李淼的《弦论史话》记载，在那期间做弦论的学生几乎要羞于承认自己在做弦论。如今的弦论虽然距离上一次革命已很远，但与当年那种状况很不相同，我个人认为，它仍在高位上。也许“如日中天”这个词太过强烈，而且太多外延，我会将之改为诸如“在弦论在基础研究中仍具有垄断地位的时候”等plain一点的说法。

（如果有所谓的第三次革命发生，其效果会与超对称被发现类似，即将曲线抬高一段时间。）

（再次强调一下：这幅图的前提是弦论最终衰落，而非预测弦论一定衰落。）

呵呵，昌海兄这个图示说明一目了然，生动有趣，给他本人奖励一下:-)

：：也许“如日中天”这个词太过强烈，而且太多外延，我会将之改为诸如“在弦论在基础研究中仍具有垄断地位的时候”等plain一点的说法。
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高能物理的基础研究中还有非常活跃的唯象研究，虽然唯象研究和实验研究很靠近，但是也存在一些和弦论交叉的地方，SUSY是一方面，另一方面，弦唯象的研究也不少，实际上，我觉得弦论不是垄断，而是寡头之一。但是在通往TOE的征途中，弦论绝对是超级垄断。但是TOE研究不等于基础研究。物理的基础研究学者中，有人向往TOE，但是更多人却比较实际，只是想探索探索TeV能标下有多少新物理，包括SUSY，Little Higgs，以及大额外维之类的BSM理论。

当然，SUSY一旦失宠，那么弦论确实死得非常快，所以那图非常形象，抖得严重些就更好了，因为物理的进展或者倒退从来不是那么平坦的，而是一波未平，一波未起，嘿嘿。

我将我上面回帖的有关内容整理扩充到一篇短文中了，标题为“超对称、弦论及弦论之可能衰落原因”（在“繁星物理笔谈录”中）。欢迎其他感兴趣的网友也来“八卦”。如果弦论真的衰落了，我们有生之年应该是可以看到那一天的。到时候谁猜得最准谁就 --


























请客。:)

有很多物理天才被吸引到弦论那里，一旦弦论失宠，也许一些不为人关注的边缘领域，会引起更多人的注意，会让人重新审视以往不受重视的idea

Let me say a few more words about string theory and SUSY.

I am not going to touch the subject whether or why string theory will go downhill. It is very likely that interesting real stringy physics lies at very high energy scale. Therefore, it is probably to say it in really hard to test it directly or falsify it directly. Therefore, whether it will go up or down base on circumstantial evidences (and weak ones usually) is really a good subject in sociology. Since that is not my field, let me refrain from making that judgement.

It is usually said that string theory predicts supersymmetry. It is a statement based on the following logic (roughly). If you get bored about bosonic string theory, or motivated by hatred towards a tachyongic state, the next thing you could try is to introduce something called worldsheet supersymmetry by introducing worldsheet fermions which together with the worldsheet boson satisfy something called D=2 superconformal algebra (Notice this is not the same as the spacetime supersymmetry, and they don't really necessarily lead to each other). Then, you work out the spectrum. Too bad, you still have tachyons. However, there is a savior. It turns out that keeping all possible states around is not really consistent. For example, it will break some of the symmetries which keep the string theory consistent. And, fortunately, there is a discrete symmetry in theory (the so called worldsheet fermion number). Therefore, we could try to consistently keep only part of the states which is even or odd under this symmetry (You cannot if this is not a symmetry since even will go to odd and odd will go to even). Therefore, we could try to do this. There are several consistent choices (type I, Typy IIA, IIB). The procedure to go to these choices goes by the name GSO projections. Anyway, once you do that, miracle! you find spacetime supersymmetry (in 10 dimensions). These are good, well understood, so-called perturbative string vacua.

There are obvious caveats in this argument. First of all,tachyons may not be as bad as we thing. It usually just mean we are probably a wrong vacuum. It has to roll to some stable vacuum. Of course, it is usually not quite known whether the new theory will have the same degrees of freedom as the old one. However, it is conceivable one can just find theories with not much change, except the tachyon is stabilized. At least, it is not obvious at all why the stable theory will have supersymmetry. Moreover, we are usually talking about the so called critical string theories (means D=26 for bosonic string and D=10 for superstring), stem from the simpliest way one knows how to make a unitary string theory. However, it is not clear at all why these are the only possibilities. In fact, there are many works about non-critical string theories and there are many examples. They don't have tachyon, and usually don't really have supersymmetry. All these things are much less explored, not because they are not likely, but because they are hard. The couplings are usually not so small. Without supersymmetry, we don't usually know what to do in the case of large coupling. However, if string theory is realized in nature, it does not have to care whether we can compute or not. Proton exists, never mind the fact that we cannot compute its mass.

Even if we start from superstring theory, the supersymmetry it possese is usually not the supersymmetry we are talking about. What we usually talk about is the so-called N=1, D=4 supersymmetry with breaking terms on the order of TeV. This gives us a solution to the so-called hierarchy problem, gives us gauge unification, etc. It is an appealing feature. That's why many people, including me, is working on it.

However, to begin with, if the supersymmetry is unbroken in the string theory (compactify on T^6, for example), it translate into D=4, N=8 supersymmetry. This is not acceptable since it is not chiral. Therefore, typically, people pick manifolds (Calabi-Yaus, for example) which only preserves N=1 supersymmetry. Then break it again at TeV scale. You see, as nice as this picture maybe, it contains a lot of assumptions and/or wishes. It is always good to wish and dream in physics. However, it is not true that one should say go to hell if one dream is broken. For example, if one is breaking supersymmetry, naively, there is no reason why some of them should survive all the way down to the low energy scale. In fact, people tried very hard. It usually takes a lot of effort to break supersymmetry at the appropriate scale. Therefore, besides our good wishes, it is not unlikely that supersymmetry in string theory is just broken at very high scale. Again, this is a scenario for which little study has been done not only because it is a little disappointing, but also it is hard to do any calculations without supersymmetry. A symmetry which is broken pretty much at the cut-off of an effective field theory should not have any implications for the low energy physics at all.

Given all these caveats, let me emphasize again low energy supersymmetry is still very appealing idea. It is appealing independent of superstring theory since it solves a lot of problems and puzzles. The picture that it comes from string theory requires several assumptions. It is still an interesting and appealing possibility. However, one should always keep those caveats in mind.

To me, string theory is appealing not only because it offers the possibility of a theory of everything, but also that everything includes in particular gravity. However, string theory is still probably a little bit distance away from acheiving that goal. That's also why I think AdS-CFT is really a very deep theoretical break through since it does says some highly non-trivial about gravity.

Actually, I really like the one-liner proof mentioned by Polchinski. I think it gives a very good explanation to the finiteness of string theory by relating it to a unique feature of the string theory: the connection between UV and IR which could be easily demonstrateby by a simple string amplitude. This is sort of argument which will convince a physicist like me.

It is probably impossible to give a rigorous proof at this moment since we don't even know the full vacua of string theory yet. In many cases, we probably don't really know the appropriate degrees of freedom yet. However, I think we could probably safely say that all known string theories (maybe one has to say perturbative) are finite.


I am amazed that Lee is criticizing string theory for lack of mathematical rigor. Besides the fact the true mathematical rigor rarely buys us anything. They are almost always after thoughts, as Polchinski point out. There is no parallel at all between string theory and 'others', since things like loop quantum gravity does not even qualified to be called a theory.

Very good review.

Lee and other LQG guys clearly used double standard while criticizing string theory. The work he himself did about emergent states from quantum spacetime is no where close to be a real demonstration, yet he consider that to be a major progress.